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Full text of "Standard substances for the calibration of viscometers"

STANDARD SUBSTANCES FOR THE CALIBRATION 
OF VISCOMETERS 



By Eugene C. Bingham and Richard F. Jackson 



CONTENTS 

Page 

I. Introduction 59 

II. Sucrose solutions 61 

1 . Purification of sucrose . . . . 61 

2 . Preparation of solutions 62 

III. Measurement of viscosity 64 

1. The viscometer 64 

2. Viscosity formula 64 

3. Calculation of constants in formula 65 

4. Calculation of the pressure 65 

5. Details in regard to instrument and measurements 69 

IV. The Centipoise 72 

V. Viscosity and fluidity of water 73 

VI. Viscosity and fluidity of ethyl alcohol-water mixtures 76 

VII. Viscosity of sucrose solutions 77 

VIII. Summary 85 

Appendixes 86 

Appendix A. — Density in grams per milliliter of mixtures of ethyl alcohol 

and water 86 

Appendix B. — Density in grams per milliliter of sucrose solutions 86 

I. INTRODUCTION 

In making measurements of viscosity in absolute units it is 
very desirable to have several substances available whose vis- 
cosities are accurately known in order that the accuracy of the 
method of measurement may be judged. Instruments whose 
results are expressed in terms of merely arbitrary numbers do 
not possess any advantage in this respect, since it is still neces- 
sary that the numbers obtained by two different instruments of 
the same type should agree, and in attaining this end the use 
of two or more substances of known viscosity is obviously of 
advantage. 

Water is naturally the most important substance for this pur- 
pose since it can be so easily obtained in a pure condition and its 
viscosities at different temperatures have been very carefully 

59 



60 Bulletin of the Bureau of Standards Voi.14 

determined. But water is ill-suited for the calibration of the 
short-capillary technical viscometer, since water is so very much 
more fluid than most oils for which these instruments were 
intended. In spite of the oft-repeated statement to the contrarv, 
the viscosities of two substances are by no means directly pro- 
portional to the times of flow of equal volumes through a given 
capillary under the same head. The chief cause of this lack of 
proportionality is the fact that the energy is not all expended in 
overcoming viscous resistance, a part of it being used up in im- 
parting kinetic energy to the fluid entering the capillary. Thus 
in the flow of water through an Engler instrument only about 10 
per cent ' of the total energy expended is used in overcoming 
viscous resistance, the remaining 90 per cent being used in impart- 
ing kinetic energy to the liquid. The presence of so large a kinetic 
energy correction renders it manifestly desirable to have at hand 
some substance of high viscosity which can easily be obtained in a 
pure condition and whose viscosity is accurately known. 

Castor oil and olive oil have been studied, but it has not been 
determined to what extent the viscosity may vary with the con- 
ditions of manufacture and exposure to light and air. 

No pure hydrocarbon is readily available which possesses suffi- 
ciently high molecular weight. Monoacid alcohols of high molec- 
ular weight, like amyl alcohol, are not cheaply and easily obtained 
in the pure and anhydrous condition. A mixture of 45 per cent 
by volume of ethyl alcohol and water has a viscosity which is 
almost exactly four times that of water at o° C. Since the viscos- 
ity of ethyl alcohol-water mixtures passes through a maximum for 
this concentration, the viscosity does not change rapidly with the 
concentration, which is a marked advantage. The viscosities of 
alcohol and water mixtures have been determined with care by 
several observers. 

When more viscous substances are desired, the poly-acid alco- 
hols are available, and of these glycerol is perhaps the best for 
the purpose. It is, however, hygroscopic and not readily obtain- 
able in the pure anhydrous condition so that the preparation of 
a solution of predetermined concentration offers some difficulty. 

The sugars are valuable substances for the purpose. They are 
not hygroscopic; they are cry stalliz able so that they may easily 
be obtained in a very pure condition. The concentration of sucrose 

1 Obtained by substituting the dimensions given in Ubbelohde's Tabellen zum Enqlerschen Viskosimeter, 
p. 24, in our equation (;) assuming the viscosity of water at 20 to be 0.01005 and the time of flow to be 51 
seconds. 



jilsoT] Viscosity Standards 61 

solutions may be determined by direct weighing of the constituents 
or from the density of the solution, or by means of the polariscope. 
Sucrose is very soluble in water, so that its solutions offer a wide 
range of viscosities. There is no concentration of sucrose in water 
which possesses the advantage of the alcoholic solution noted 
above, whose viscosity is independent of the exact concentration; 
hence it is necessary to guard the sucrose solutions against evapo- 
ration. Fortunately the technique of handling sucrose solutions 
has already been carefully worked out. 2 

The viscosity of sucrose solutions has repeatedly been the 
object of study, but the recent discovery 3 of important sources 
of error in viscosity measurement which have hitherto remained 
undetected makes it desirable that these solutions be the object 
of still further research. Fortunately the data for water are suffi- 
ciently complete so that the more important corrections thus far 
recognized can all be made with sufficient certainty for our present 
purposes. 

II. SUCROSE SOLUTIONS 

1. PURIFICATION OF SUCROSE 

The sucrose used in preparing the solutions was purified by 
crystallization from aqueous solution in the manner previously 
described by Bates and Jackson. 4 Their procedure in outline was 
as follows: The material, a quantity of good granulated cane sugar 
of commerce, was dissolved in an equal weight of distilled water, 
clarified with a small quantity of washed ''alumina cream/' 
filtered and boiled in vacuo at a temperature of about 35 ° C until 
a concentration of 80 per cent was reached. The supersaturated 
sirup was seeded with a few crystals of sucrose and allowed to 
crystallize while in continuous motion. The crystals were sepa- 
rated from the mother liquor in a powerful centrifugal machine and 
were washed with aqueous alcohol. The crystallization was 
repeated until no evidence of impurity could be obtained. 

The progress of the purification was studied and is described in 
the paper referred to. They found that sucrose prepared by this 
method contained less than 0.002 per cent of ash. The reducing 
substances, aside from sucrose itself, were of the order of 0.00 1 
per cent if present at all. The optical rotary power of the material 
remained unchanged after fractional crystallization from aqueous 

2 This Bulletin, 10, p. S3T, 1914- 

* J. Am. Chem. Soc.,88, p. 27; 1916. 

* This Bulletin, 13, p. 75, 1916; Scientific PaperNo. 268. 



62 Bulletin of the Bureau of Standards Vol. 14 

solution and after precipitation with ethyl and methyl alcohol. 
The specific rotation of the substance in the concentration of the 
normal 5 solution was found for X = 5892.5 A to be 66?529, or 
slightly higher than the mean of the measurements of Tollens and 
of Nasini and Villavecchia who found for it 66? 502. 6 The sugar 
used in the present investigation was prepared from the same 
source and possessed the same rotary power as that prepared by 
Bates and Jackson. 

2. PREPARATION OF SOLUTIONS 

In preparing the solutions for the viscosity measurements the 
constituents were weighed into a flask and the sugar dissolved. 
The solution in general was not completely free from dust par- 
ticles. The amount of dust was too small to be weighable, but by 
accumulation in the capillary of the viscometer could readily have 
affected the time of flow. The solution was consequently poured 
on filters of hardened filter paper and repeatedly poured back to 
remove shreds acquired from the paper. The clear solution was 
finally poured through a funnel into a calibrated volumetric flask. 

Three measurements of the concentrations of the solutions were 
made, two of which depended upon the solution density and one 
upon the rotary power. 

The volumetric flasks which were used possessed graduated 
necks about 6 mm inside diameter. The graduations were 10 in 
number 0.02 ml apart. The interval between successive marks 
could be estimated to one-tenth of one division. The original 
solution was poured into the flask to some point on the scale, and 
flask and solution immersed in the water of a thermostat. When 
sufficient time had elapsed for the solution to assume the tempera- 
ture of 2o?oo, its volume was observed. From these data the 
density of the solution was calculated. Then by comparison with 
the tables of the Kaiserliche Normal Eichungs Kommission, the 
per cent composition of the solution was obtained. 

The second measurement, made after the sample for viscometer 
measurement was taken, consisted of determining the density of 
the approximately normal solution taken for polarization. A 
portion of the original solution was poured into another weighed 
volumetric flask, and flask and solution weighed. Enough of the 
solution was taken to correspond to about 26 g of sucrose in 100 

5 The normal concentration is 26 g in 100 ml of solution in accordance with the usage in sugar analysis. 
9 This Bulletin, It, p. 125; 1916. 



Bingham! 
Jackson J 



Viscosity Standards 



63 



ml. The sides of the flask were rinsed down into the solution and 
the latter diluted nearly to the capacity of the flask. The tem- 
perature was adjusted and the flask filled to the mark and weighed. 
The third measurement consisted of a polarization of the approxi- 
mately normal solution on a quartz-wedge saccharimeter. The 
thoroughly mixed solution was poured into polariscope tubes of 
known length and polarized at a fixed temperature. The read- 
ing of the saccharimeter was controlled by comparison with 
quartz plates No. 1 and No. 3, which are the primary standards 
of this Bureau referred to and described in the paper by Bates 
and Jackson. In determining the sugar value of these plates the 
conversion factor 34?62o was used instead of the erroneous 

34°657. 

In addition to the solutions prepared from purified sucrose one 
was prepared from a quantity of good granulated sugar of com- 
merce in order to determine whether or not this generally avail- 
able material would be suitable for standardization of instruments 
of ordinary precision. The substance after filtration contained 
but 0.012 per cent of ash. Its concentration was determined 
from the density of the solution by the second method described 
above, from its polarization, and from the reading of a standard- 
ized hydrometer. Since the effect of the impurities upon the 
fluidity was problematical, no attempt was made to apply correc- 
tions for them. The mean value of the three determinations was 
taken for the concentration. It is apparent that a calibrated 
hydrometer gives a satisfactory determination of the concentra- 
tion. 

The summary of the analyses is given in Table 1 . 

TABLE 1 
Analytical Data on Sucrose Solutions 





Percentage concentration by weight in vacuo 


Solution 


By density 

of original 

solution 


By density 
of solution 
taken for 
polarization 


By polari- 
zation 


By stand- 
ard hy- 
drometer 


Mean 


No. 1 


39.96 
40.00 
59.97 
20. 003 


40.01 
39.97 
59.93 


39 99 
39.99 
59.93 
20. 011 
60.12 




39 99 


No. 2 




39 99 


No. 3 




59 94 


No. 4 




20 007 


No. 5 


60.15 


60.24 


60 17 









o Granulated sugar of commerce. 



20172°— 17- 



6 4 







Fig. i. — The viscometer. 



Bulletin oj the Bureau of Standards voi.14 

III. MEASUREMENTS OF VISCOSITY 

1. THE VISCOMETER 

The viscometer used in this investigation 
is shown in Fig. i. drawn to scale. The 
method of making a measurement was as 
follows: The clean and dry instrument was 
rilled from H to .4 with the liquid to be 
measured, the surplus liquid overflowing into 
the trap at A. The liquid was introduced 
by means of a pipette drawn out into a fine 
tube. The left limb was connected with a 
tank filled with air under a pressure which 
could be measured on a water manometer, 
the right limb already having been connected 
with the air. The time which the meniscus 
required in falling from B to D was taken as 
the time of flow. The liquid was then in posi- 
tion for an observation of the time of flow in 
the opposite direction. When the tempera- 
ture was raised, the volume was again ad- 
justed by causing the surplus to run over 
into the trap. 

2. VISCOSITY FORMULA 

Knowing the time of flow, t, the pres- 
sure, p, and the two constants of the in- 
strument, C and C, it became possible to 
calculate the viscosity, 77, of the liquid for 
the temperature of observation, using the 
formula 

v = Cpt-C' P jt (1) 

The value of the density, p, does not need 
to be accurately known, since it appears 
only in the term which represents the 
kinetic energy correction, which in our ex- 
periments was purposely kept small in order 
that the slight uncertainties in regard to the 
value of the correction term might be ren- 
dered nesrlible. 



fJS&T] Viscosity Standards 65 

The complete viscosity formula for the capillary tube method is 

irgr^pt mnpv ( . ? 

r? "87;(/+X)~87r/(/ + X) (2) 

where v is the volume of flow, r is the radius, and / the length of 
the capillary, X is a correction to be made to the length on account 
of viscous resistance outside of the capillary and to the distortion 
of the stream lines just within the entrance to the capillary. 
According to all of the evidence at hand this correction is neg- 
ligible when the capillary is very long in comparison with the 
radius of the tube. The number of capillaries in series is repre- 
sented by n, while misa constant whose value is being generally 
accepted to be about 1.12. 7 

3. CALCULATION OF CONSTANTS IN FORMULA 

From the approximate dimensions ^ = 4.00 and / = 7.50 we can 
calculate the value of C 

„, mnV , , . 

c = 87r = °-° 2376 (3) 

Observing the rate of flow of pure water at 20 C under a given 
pressure, and taking the absolute viscosity of water at this tem- 
perature to be 0.01005, we may calculate the value of C 

4. CALCULATION OF THE PRESSURE 

The pressure used in the above formulas is expressed in grams 
per square centimeter. It is obtained as follows : If the height read 
on the manometer scale — corrected for scale error, if necessary — 
is h , Fig. 2, and the density of the liquid in the manometer is p , 
then the pressure is h p Q . But this pressure is subject to several 
corrections which may be small but must be taken into considera- 
tion. (1) The correction for buoyancy of the air is — h p air. (2) 
The air in the closed limb of the manometer is under pressure and 
is therefore denser than the air outside. If the middle of the bulbs 
of the viscometer were at the level of the middle of the manometer 

the correction for this cause would amount to — - p B ir — ™ (3) 

2 1033 

7 Zs. physik. Chem., 80, p. 681; 1912. 



66 



Bulletin of the Bureau of Sta?idards 



Voi.14 



If, however, the middle point of the manometer is at a distance h' 
below the middle of the viscometer, there is a further correction 



-h'p 



air 



I033 



• (4) There is a further correction for the hydrostatic 



head within the viscometer, arising from the fact that it is impos- 
sible to construct an instrument in which the two bulbs are of 
exactly the same shape and size or at the same height. If the 




Fig. 2. — Diagram illustrating the method of estimating the pressure used in a viscosity 

determination. 

hydrostatic head is h u Fig. 2, obtained as will be described later, 
the pressure correction w r ill be h x p and this may be either negative 
or positive, dependent upon the limb to which the pressure is being 
admitted; that is, whether the left limb is emptying or filling. 

Making these corrections we have for the assumed constant 
pressure 

h 



po = h p — h pi ir 



ho 2 



2^66 *l'± &1 *tr — 



±h l p 



(5) 



Bingkaml 
Jackson J 



Viscosity Standards 



67 



We have calculated Tables 2 and 3 which simplify the use of the 
above formula, and cause the formula to take the form 

p = h ±h lP -K±L (6) 8 

In this formula h is the height in centimeters of the water column 
in the manometer, k ± is the hydrostatic head, and p the density 
of the liquid within the viscometer, L is the correction for the 
difference of level between viscometer and manometer. This 
correction may usually be made negligible in the construction of the 
apparatus, but if necessary, the corrections corresponding to 
different values of h' and h may be obtained from Table 2. Table 
3 contains the values of K, including the corrections for tempera- 
ture, buoyancy, etc., for the different temperatures and pressures. 
A single example will serve to show the method of using the 
tables. In our viscometer L was negligible, but the hydrostatic 
head was /^ =0.2 cm, the right bulb of the viscometer being higher 
than the left, so that, for a 40 per cent sugar solution at 20 C, 
p = i.i76, and at a pressure read on the manometer of & = 269.5 
cm at 23 C, the correction is (0.77+0.22 +0.03) +0.24 = 1.3 cm 9 
when the pressure is on the left limb, or (0.77+0.22+0.03) — 
0.24 = 0.8 cm when the pressure is on the right limb of the 
viscometer. 

TABLE 2 
Values of L 



h' in centimeters 


h in centimeters 


100 


200 


300 


50 


0.01 
.01 
.03 
.04 


0.01 
.03 
.05 
.08 


0.02 


100 ; 


.04 


200 


.08 


300 


.11 







(5) The applied pressure p is not necessarily the true average 
pressure to be used in the viscosity formula, hence a further cor- 
rection may be necessary. Bingham, Schlesinger, and Coleman 9 \ 
have shown that if the bulbs of the viscometer were cylindrical 
in shape and of the height h, the true average pressure p, obtained 
by integration, would be 

0.8686&P 

P = 



loe h±h£ 



(7) 



AoVair 

8 In obtaining (6) from (5) K=ho— hoPo+hop*ii+——7jr' 

9 The figures within the parenthesis are the interpolated value of . K 
8 » J. Amer. Chem. Soc., 37, p. 27; 1916. 



68 



Bulletin of the Bureau of Standards 



Vol. 14 



but the difference between p and p becomes less than 0.05 per 
cent — that is, negligible for ordinary purposes — when the value of 
p becomes as great as 30 times that of Up. They have shown 
how to obtain the value of h when this correction is not negligible 
and the bulbs of the viscometer are not true c vlinders. 



TABLE 3 
Values of K 



Temperature, 


Manometer reading, ho. 


C 


10 


20 


N 


40 


50 


60 


70 


80 


M 


100 


200 


300 


5 


0.013 
.016 
.017 
.018 
.019 
.020 
.022 
.023 
.025 
.027 
.029 
.031 
.033 
.035 
.037 
.040 
.042 
.045 
.048 
.050 
.053 
.056 
.059 
.062 
.066 
.069 


0.025 
.030 
.032 
.035 
.037 
.040 
.043 
.ON 
.049 
.053 
.057 
.060 
.065 
.069 
.074 
.079 
.084 
.089 
.094 
.100 
.105 
.111 
.117 
.124 
.130 
.137 


0.039 
.045 
.050 
.053 
.057 
.061 
.065 
.070 
.075 
.080 
.086 
.092 
.098 
.105 
.112 
.119 
.127 
.135 
.143 
.151 
.160 
.169 
.178 
.188 
.197 
.207 


0.053 
.064 
.068 
.072 
.077 
.082 
.088 
.094 
.101 
.108 
.116 
.124 
.132 
.141 
.151 
.160 
.170 
.181 
.191 
.202 
.214 
.226 
.239 
.251 
.264 
.277 


0.066 
.078 
.083 
.089 
.095 
.102 
.110 
.118 
.126 
.135 
.144 
.154 
.165 
.176 
.188 
.200 
.212 
.225 
.239 
.253 
.268 
.283 
.298 
.314 
.330 
.346 


0.079 
.095 
.101 
.106 
.115 
.123 
.131 
.140 
.150 
.161 
.173 
.185 
.198 
.211 
.225 
.240 
.255 
.270 
.286 
.303 
.321 
.339 
.357 
.376 
.395 
.415 


0.094 
.112 
.119 
.126 
.135 
.144 
.154 
.165 
.176 

.us 

.203 
.217 
.232 
.247 
.264 
.281 
.298 
.316 
.335 
.355 
.375 
.396 
.417 
.439 
.462 
.485 


0.108 
.129 
.137 
.145 
.155 
.165 
.177 
.189 
.203 
.217 
.233 
.249 
.265 
.282 
.301 
.321 
.341 
.362 
.383 
.405 
.429 
.453 
.478 
.503 
.529 
.555 


a 122 

.145 
.154 
.163 
.175 
.187 
.199 
.212 
.228 
.245 
.262 
.280 
.299 
.319 
.341 
.363 
.385 
.408 
.432 
.458 
.484 
.511 
.538 
.567 
.595 
.625 


0.136 
.162 
.172 
.183 
.195 
.208 
.222 
.238 
.255 
.273 
.292 
.312 
.333 
.355 
.379 
.403 
.428 
.454 
.481 
.509 
.538 
.568 
.599 
.630 
.662 
.695 


0.285 
.337 
.357 
.379 
.403 
.429 
.457 
.439 
.523 
.559 
.597 
.637 
.679 
.723 
.770 
.819 
.869 
.921 
.975 
1.031 
1.089 
1.149 
1.210 
1.273 
1.337 
1.403 


0.482 


10 


.533 


11 


.563 


12 


.596 


13 


.632 


14 


.671 


15 


.713 


16 


.761 


17 


.812 


18 


.866 


19 


.923 


2*3 


.983 


21 


1.046 


22 


1.113 


23 


1.184 


24 


1.256 


25 


1.331 


26 


1.409 


27 


1.490 


28 


1.574 


29 


1.661 


30 


1.751 


31 


1.842 


32 

33 

34 


1.937 
2.033 
2.132 



To obtain the hydrostatic head h x , we determine the times of 
flow f, and /, for some substance, such as water at 20 C, for the 
right and left limbs of the instrument, respectively, with a given 
pressure, which is p u corrected except for the hydrostatic head. 
We have the equations 



and 



*♦*,.*§* 
*-*,-*£& 



jZg™] Viscosity Standards 69 

hence 

In obtaining h x it is sufficient to use the approximate value of C, 
obtained by using p 1 in place of p in equation 4. 

5. DETAILS IN REGARD TO INSTRUMENT AND MEASUREMENTS 

The bulbs of the viscometer were made as short as practicable 
in order that the difference between the applied pressure and the 
true average pressure might be a minimum. The distance between 
the marks B and D was 3.0 cm. 

The bulbs were made conical in shape in order to obtain the 
necessary volume while avoiding nearly horizontal surfaces which 
might cause faulty drainage. Drainage troubles were further 
obviated by having the part of the instrument directly above the 
point B in Fig. 1, similar in shape to the part above the point D. 
By always reading the volume of flow on the left limb, irrespective 
of whether the direction of flow is from left to right or vice versa, 
we measure the time of flow of the volume which the bulb C 
delivers in the former case but of the capacity of the bulb in the 
latter case. Thus any differences in the viscosity calculated from 
the times of filling and emptying of this bulb may serve as a test 
of the completeness of the drainage. A further test can of course 
be made by making observations of the time of flow at different 
pressures. 10 

The capillary tube was cut off squarely and sealed into the 
instrument so as to avoid a trumpet-shaped opening in order that 
there may be no doubt about the maximum value of the kinetic 
energy correction being applicable. 

In order to prove that the corrections made are trustworthy, a 
series of observations were made on water at 25 ° C, using a con- 
siderable range of pressures. Table 4 shows that the calculated 
viscosity is satisfactorily constant. 

10 By using an instrument similar to the one described in this Bulletin, 12, Scientific Paper No. 278. 
p. 309 (1916), all possibility of error due to bad drainage can be obviated, but in the present investiga- 
tion that type of instrument is far less convenient than the one adopted and fortunately its use is 
unnecessary. 



7o 



Bulletin of the Bureau of Standards 



Vol. 14 



TABLE 4 

Viscosity of Water at 25° C Calculated from the Constants Obtained from Observations 
on the Rate of Flow of Water at 20° C, Assuming the Viscosity at this Temperature to 
be 0.01005 (C=0.000000 14307 and C'=0.02376) 



Limb 



R 
L 
R 
L 
R 
L 
R 
L 
R 
L 
R 
L 



t 


P 


Sees. 


g/cm J 


570.9 


110.04 


572.9 


109.65 


570.6 


110.04 


572.9 


109. 65 


571.3 


110.04 


572.4 


109.65 


819.2 


76.76 


821.2 


76.37 


818.2 


76.81 


820.6 


76.42 


399.4 


157. 56 


400.6 


157. 19 



g/cm J 
109.53 
109.14 
109.53 
109.14 
109.53 
109.14 
76.51 
76.12 
76.56 
76.17 
156. 53 
156.16 



0.008946 
.008946 
.008942 
.008946 
.008952 
.008938 
.008968 
.008944 
.008963 
.008943 
.008944 
.008950 



Limb 



Sees. 
399.6 
400.2 
306.5 
307.6 
306.5 
308.1 
274.8 
276.8 
274.4 
274.8 
273.4 
275.1 



g/cm» 

157. 59 
157. 22 
205. 43 
205.04 
205.44 
205. 05 
229.64 

228. 08 

229. 48 
229. 58 
230.45 
229. 72 



g/cm» 

156.56 
156.19 
203. 67 
203.28 
203.68 
203.29 
227. 45 
225. 92 
227. 29 

227. 39 

228. 24 
227. 53 



0. 008951 
. 008943 
.008931 
.008946 
.008932 
.008961 
.008943 
.008947 
.008923 
.008940 
.008928 
. 008955 



In the above table, as well as in succeeding tables, we have 
given not merely the true average pressure p, but also the part of 
this pressure P, which is used up solely in overcoming viscous 
resistance. It is calculated by means of the formula 



whence we have that 



l = Cpt-C'p/t = CPt 



P = p- 



a 2 



(9) 



The object in recording both p and P is in order to afford a 
measure of the kinetic energy correction. 

The viscometer was attached to a brass frame which fitted in 
grooves on the side of the bath shown in Fig. 3, so that the vis- 
cometer was necessarily always in the same position. A part of 
the viscometer always projected above the bath, so that any 
vapor rising from the solution would tend to condense and run 
back. It may be remarked that the experiment was tried of 
repeating a measurement after heating a solution for several 
hours and then cooling, but without noteworthy effect. 

The temperature was read by means of a telescope to one one- 
hundredth of a degree centigrade. As the thermometer had 
been calibrated at the Reichsanstalt, it was unnecessary to rede- 
termine its corrections, but its ice point was determined before 
and after the investigation. At the two highest temperatures 
used a part of the stem of the thermometer was exposed, for which 
a correction was also made. 



Bingkaml 
Jackson * 



Viscosity Standards 



71 



C-'v 




Fig. 3. — Detail of bath and frame with viscometer in position 



7- Bulletin of the Bureau of Standards Vot.u 

The time was measured on an Agassiz stop watch which had 
been tested by this Bureau and given a rating of 56.2 in class A. u 
It was losing at the rate of a minute in a month during the time 
of the experiments. 

IV. THE CENTIPOISE 

It has been common practice to record viscosities in other 
than absolute units. There are at least three reasons for using 
specific viscosities rather than absolute viscosities. Absolute 
viscosities are often inconveniently small fractions, necessitating 
the use of many ciphers. We naturally compare the viscosity of 
any liquid with that of water, which is usually used as the stand- 
ard, hence the specific viscosity makes an immediate impression 
upon the mind which the absolute viscosity does not until after 
considerable practice. Finally, the so-called specific viscosi- 
ties are often arbitral*}- numbers which are not reducible, or at 
least not easily reducible, to absolute units. Thus in the use of 
most technical instruments such as those of Engler and Saybolt, 
the so-called viscosities are recorded in terms of arbitrary num- 
bers known as Engler degrees or Saybolt seconds, respectively. 
These numbers are far from being proportional to the absolute 
viscosity, and the absolute viscosity is not in any way calculable 
without a supplementary determination of the density, the 
determination of which is often omitted. 

It is quite evident that in studying the relation of viscosity to 
other properties it is the true absolute viscosity that is desired. 
This is the strongest possible argument in favor of giving up the 
use of purely arbitrary numbers and expressing all results in 
absolute measure. Moreover, whether the specific viscosities 
are reducible to absolute units or not it is awkward to make com- 
parison between specific viscosities based upon different standards. 
Thus, when one worker uses water at o° C as his standard it is 
not easy to compare his work with that of another worker who 
used as a standard water at 25 C. or either of these with results 
expressed in absolute units. 

When two liquids having the same viscosity as measured on one 
instrument are measured in a different type of viscometer it has 
often been noted that the two liquids have quite different apparent 
specific viscosities. This arises from the fact that, in calculating 
the specific viscosity, important corrections are not taken into 
account which affect the two instruments differently. Thus, it is 

u Circular No. 51. Bureau of Standards. 



/ST] Viscosity Standards 73 

an objection to the use of specific viscosities that it has heretofore 
encouraged slovenly thinking in regard to the subject of viscosity 
measurement. 

These views as to the relative merits of specific or absolute units 
are not as irreconcilable as may seem at first. It can probably be 
agreed that all viscosity measurements should be made under con- 
ditions such that the results can be expressed in absolute units. It 
is further desirable that, if specific viscosities be used, the same sub- 
stance be taken as standard by all and that the absolute viscosity 
of the standard be definitely agreed upon, just as there is general 
agreement in the acceptance of atomic weights. If the suggestion 
of Deeley and Parr 12 is accepted, and the absolute cgs unit of vis- 
cosity be known as the " poise," then it is convenient to use the 
submultiple of this unit, which is one-hundredth as large, and 
which may therefore properly be called the centipoise (cp) . It so 
happens that the centipoise is almost exactly the viscosity of water 
at 20 C, hence viscosities expressed as centipoises have the added 
advantage of being at the same time the specific viscosity of the 
substance referred to water as standard at almost exactly 20 C. 

V. VISCOSITY AND FLUIDITY OF WATER 

Previous determinations of the absolute viscosity of water and 
other substances have neglected to take into account the possible 
difference between the mean applied pressure and the true average 
pressure. It has therefore seemed desirable to go over the data 
available and make the correction where necessary and practicable. 

Thorpe and Rodger 13 calculated their viscosities on the assump- 
tion that m = 1. 00 instead of the more generally accepted value 14 
w = i.i2. They also calculated the viscosity of water from the 
observations of Poiseuille, 15 Sprung, 16 and Slotte 17 on the same 
assumption, hence it has seemed desirable to go over this data 
and make the needed correction. The error in the true average 
pressure and the error in the value of m are both in the same 
direction, both tending to make the substance appear to be more 
viscous than it really is. In a few instances the error amounts 
to as much as 0.3 per cent. 

In arriving at the most probable values for the viscosity of 
water, it is important to observe that Poiseuille is usually credited 

12 Phil. Mag. [6], 26, p. 85; 1913. 

1S Phil. Trans., 185A, p. 397; 1894. 

"Seep. 6 S . 

15 Mem. present, par divers Savants a l'academie Roy. des Sciences de l'lnst. de France, 9, p. 4.53; 1840. 

18 Pogg. Ann., 159, p. 1; 1876. 

" Wied. Ann., 20, p. 357; i88ju 



74 



Bulletin oj the Bureau of Standards 



1W. 14 



with one series of observations from o° to 45 °, whereas he actually 
made observations over this range of temperatures with four 
different capillaries, and as there is no reason for supposing that 
his observations were any less accurate than were those of his 
successors, we have recalculated his data entire. 

Hosking 18 does not give sufficient data to permit a recalculation 
to be made, but as he adjusted the values of m and X in such a way 
as to get concordant values of viscosities at different pressures, it 
seems proper to include his values as they are recorded by him. 

TABLE 5 
Viscosity of Water in Centipoises as Determined by Different Observers 



Tempera- 
ture, C C 




Poteeuille 




| 

Thorpe Bing- 
<?T»mnff Slotte ' and Hosk- ham 


Aver- 


Calcu- 
lated by 


A* C D' E 




Rod- ing and 
ger Whiter 

1 


age 


for- 
mula 





1.7900 




1.7944 


1.777 
1.5089 
1.2995 
1.1334 
.9978 
.8947 
.8183 


1.807 
1.523 
1.313 
1.143 
1.007 
.895 
.802 


1.7766 
1.5083 
1.3014 
1. 1324 
1.0005 
.8900 
.7965 


1.7928 
1.522 
1. 3105 


1.7960 
1. 5241 
1.3002 


1.7887 
1.5155 
1.3061 
1.1406 
1.0046 
.8941 
.8019 


1. 7921 


5 


1. 5108 
1.3045 
1.1385 
1.0028 
.8900 
.7958 
.7154 
.6466 
.5867 


1. 5137 
1.3078 
1.1464 
1.0073 
.8964 
.8016 
.7194 
.6523 
.5934 


1.5143 
1.3088 
1.1465 
1.0063 
.8966 
.8011 
.7190 
.6508 
.5937 


1. 5142 
1.3088 
1.1456 
1.0087 
.8973 
.8027 


1.5188 


10 


1.3077 


15 


1.142 ! 1.1373 
1.006 1.0054 
. 8S26 . 8940 


1. 1404 


20 


1.0050 


25 


.8937 


30 


.800 


.7991 


.8007 


35 


. 7207 I . 7216 
. 6531 ! . 6558 
.5932 .6001 


.723 .7190 
. 656 . 6525 
.601 .5959 
.552 .5464 
.509 .5044 
. 471 . 4676 


.724 

.657 

.600 

.5500 

.508 

.469 

.436 

.406 

.380 

.356 

.335 

.316 

.300 


.7223 
.6557 
.5984 
.5491 


. 7205 - 7225 


40 


.6533 
.5958 

.5497 


.6560 


45 


.5988 


50 






.5512 


.5494 


55 










. 5073 - 5072 


.5064 


60 












.4728 
.4362 
.4069 
.3794 
.3558 
.3337 
.3133 
.2983 


.4701 
.4359 
.4062 
.3794 
.3556 
.3341 
.3146 
.2981 
.2821 


.4688 


65 












.437 


.4343 


.4355 


70 












. MS 
.380 
.356 
.334 
.315 


.4048 
.3782 
.3547 
.3336 
.3140 
.2970 
.2814 


.4061 


75 












.3799 


80 












.3565 












.3355 


90 








.3165 


,5 









.297 
.281 


.2994 


100 






. 2838 















° Zs. physik. Chem.. 83, p. 641; 1913. 



In next to the last column of Table 5 are given the averages of 
the values of the different observers. In the last column are given 
the values given by the formula 

B 



t = A(<P-D)-C- 



6-rD 



(10) 



which has been shown to be capable of expressing quite accurately 
the fluidity of liquids over a range of temperature, A , B, C, and D 
being arbitrary constants, and <f> being the fluidity in cgs units. We 



Phil. Mag. [c], 17, p. 502. 1909; 18, p. :6c. 1909. 



Bingham! 
Jackson J 



Viscosity Standards 



75 



have taken A =0.23275, 5 = 8676.8, C = 8.435, and D = i2o. The 
calculated values are for the most part very close to the average 
observed values. This is particularly true between 5 and 8o°. 
It seems probable, therefore, that in taking 1.005 C P as tne vis- 
cosity of water at 20 C all of the figures are significant. 

It is often desirable to know the viscosity of water at other than 
the 5 -degree intervals given above, hence we have calculated the 
fluidity and viscosity of water for every degree between o° and 
ioo°, using equation (10) in the form 

= 2.i482{(^-8.435)+V8o78.4 + (^-8. 4 35) 2 }-i2o 

TABLE 6 

Fluidity and Viscosity of Water Calculated by Formula for Every Degree Between 0° 

and 100° C 



Temperature, 
°C 


Flu- 
idity 


Vis- 
cosity 
incp 


Temperature, 
°C 


Flu- 
idity 


Vis- 
cosity 
incp 


1 

Temperature, 
°C 


Flu- 
idity 


Vis- 
cosity 
incp 





55.80 
57.76 
59.78 
61.76 
63.80 
65.84 
67.90 
70.01 
72.15 
74.28 
76.47 
78.66 
80.89 
83.14 
85.40 
87.69 
90.00 
92.35 
94.71 
97.10 
99.50 
100.00 
101.94 
104. 40 
106. 86 
109. 38 
111.91 
114. 45 
117. 03 
119. 62 
122. 25 
124. 89 
127. 54 
130. 22 


1. 7921 
1. 7313 
1. 6728 
1. 6191 
1. 5674 
1. 5188 
1. 4728 
1. 4284 
1. 3860 
1. 3462 
1. 3077 
1. 2713 
1. 2363 
1. 2028 
1. 1709 
1. 1404 
1.1111 
1. 0828 
1. 0559 
1.0299 
1. 0050 
1.0000 
.9810 
.9579 
.9358 
.9142 
.8937 
.8737 
.8545 
.8360 
.8180 
.8007 
.7840 
.7679 


33 


132. 93 
135. 66 
138.40 
141. 15 
143. 95 
146. 76 
149. 60 
152. 45 
155. 30 
158. 20 
161. 11 
164. 02 
167. 00 
169. 97 
172. 95 
175. 95 
178. 95 
182. 00 
185. 05 
188.14 
191. 23 
194. 34 
197. 45 
200. 62 
203. 78 
206. 95 
210. 13 
213. 33 
216. 54 
219. 80 
223. 07 
226. 34 
229.64 
232. 94 


0. 7523 
.7371 
.7225 
.7085 
.6947 
.6814 
.6685 
.6560 
.6439 
.6321 
.6207 
.6097 
.5988 
.5883 
.5782 
.5683 
.5588 
.5494 
.5404 
.5315 
.5229 
.5146 
.5064 
.4985 
.4907 
.4832 
.4759 
.4688 
.4618 
.4550 
.4483 
.4418 
.4355 
.4293 


67 


236. 25 
239. 57 
242. 91 
246. 26 
249. 63 
253. 02 
256. 42 
259. 82 
263. 25 
266. 67 

270. 12 
273. 57 
277. 04 
280. 53 
284. 03 
287. 53 
291. 03 
294. 54 
298. 06 
301. 63 
305. 21 
308. 78 
312. 35 
315.92 
319. 53 

323. 13 
326. 74 
330. 38 
334. 01 
337. 65 
341. 30 
344. 96 
348. 63 
352. 30 


0. 4233 


1...; 


34 


68 


.4174 


2 


35 


69 


.4117 


3 


36 


70 


.4061 


4 


37 


71 


.4006 


5 


38 


72 


.3952 


6 


39 


73 


.3900 


7 


40 


74 


.3849 


8 


41 


75 


.3799 


9 


42 


76 


.3750 


10 


43 


77 


.3702 


11 


44 


78 


.3655 


12 


45 


79 


.3610 


13 


46 


80 


.3565 


14 


47 


81 


.3521 


15 


48 


82 


.3478 


16 


49 


83 


.3436 


17 


50 


84 


.3395 


18 


51 . 


85 


.3355 


19 


52 


86 


.3315 


20 


53 


87 


.3276 


20.20 


54 


88 


.3239 


21 


55 


89 


.3202 


22 


56 


90 


.3165 


23 


57 


91 


.3130 


24 


58 


92 


.3095 


25 


59 


93 


.3060 


26 


60 


94 


.3027 


27 


61 


95 .. 


.2994 


28 


62 


96 


.2962 


29 


63 


97 


.2930 


30 


64 


98 


.2899 


31 


65 


99 


.2868 


32 


66 


100 


.2838 











76 



Bulletin of the Bureau oj Standards 



Vol. 14 



VI. VISCOSITY AND FLUIDITY OF ETHYL ALCOHOL- WATER 

MIXTURES 

It was stated above that ethyl alcohol-water mixtures possess 
certain advantages for the purpose of testing viscometers. They 
have already been used successfully for this purpose by AYinslow 
H. Herschel, of this Bureau. 

The fluidities of ethyl alcohol-water mixtures have already been 
determined by various observers, the data being brought together 
in a paper by Bingham, White, Thomas, and Cadwell. 19 The 
older data is subject to some uncertainty on account of various 
circumstances, hence in getting the average some system of 
weighting seemed necessary. In obtaining the average values 
given in Tables 7 and S the data of Bingham and Thomas 19 was 
given a weight of three, that of Xoack 2n of two, and that of 
Traube,- 1 Pagliani, and Batelli," and Stephan :3 of one. 

TABLE 7 
Fluidity of Alcohol-Water Mixtures 



Tem- 
perature, 



Weight, percentage of ethyl alcohol 



II 



:■: 



30 



GO 70 80 



?■: 



Volume, percentage of ethyl alcohol at 25° C 



12.36 24.1 



C. 

5.. 
10.. 
15.. 
20.. 
25.. 
30.. 
35.. 
40.. 

45 167.0 

50 182.0 

55 1 197.4 

60 213.3 

65 1 229.6 

70.. 



55.8 
65.8 
76.5 
87.7 
99.5 
111.9 
124.9 
138.4 
152.4 



. 246.3 

75 263.2 

80 280.5 



30.2 

38.8 

45.9 

55.8 

65.0 

75.6 

86.2 

99.4 

110.2 

123.2 

136.3 

150.9 

164.3 

180.5 

194.5 

210.2 

232.7 



18.8 

24.6 

31.6 

38.2 

45.8 

55.1 

64.4 

75.1 

86.2 

98.5 

110.2 

122.9 

135.8 

150.1 

164.5 

178.8 

198.1 



35.23 



14.4 

18.9 

24.7 

30.7 

36.9 

45.9 

53.4 

63.3 

73.1 

84.1 

95.2 

107.6 

119.9 

133.0 

146.4 

160.3 

176.4 



^5.83 50.94 55.93 



65. 56 I 74. 80 



13.8 
17.8 

22.8 

28.4 

34.7 

42.5 

50.0 

58.6 

67.9 

77.9 

89.0 

100.7 

113.0 

125.3 

138.0 

151.5 

167.1 



14.0 

17.9 

22.8 

28.3 

34.4 

42.5 

49.4 

58.3 

67.5 

77.6 

88.3 

100.2 

112.0 

124.7 

137.5 

150.8 

166.5 



14.4 

18.2 
23.0 
23.5 

41.9 

49.5 . 

57.7 

66.9 

76.5 

87.1 

98.4 

110.3 

122.6 

135.2 

148.9 

164.1 



15.2* 

19.0 

23.9 

29.1 

34.8 

41.7 

49.6 

58.0 

66.7 

77.3 

86.6 

98.0 

109.5 

122.3 

135.1 

148.7 

163.5 



17.4 
21.6 
26.5 
31.8 
37.4 
44.6 
51.9 
60.1 
69.1 
78.7 
85.7 
100.3 

no.8 ; 

124.1 
137.2 
150.8 
165.7 



21.0 

25.6 

30.6 

36.1 

42.2 

49.1 

56.6 

65.4 

74.4 

84.1 

94.2 

106.0 

116.8 

130.6 

143.9 

157.1 



92.01 100 



27.1 

32.0 

36.9 

43.3 

49.8 

57.2 

65.3 

73.8 

83.1 

92.5 

103.3 

115.3 

126.7 

140.7 

153.9 

166.6 



36.6 

43.3 

47.6 

55.5 

62.1 

70.2 

78.2 

87.2 

96.6 

106.5 

117.9 

130.8 

142.1 

156.0 

169.9 

183.0 



100 



56.4 

61.6 

68.2 

75.1 

83.3 

91.2 

99.7 

109.4 

119.9 

130.8 

142.5 

155.2 

168.9 

181.5 

198.6 

212.5 



" Zs. physik. Chem., 83, p. 644; 1913. 

M Wied. Ann.. 27, p. 289; 18S6. 

■ Bcr. d. deutsch. chem. Gesell., 19, p. S71; 1886. 

*= Atti. d. R. Ace. di Torino, 20, p. 845; 1885. 

» Wien. Ber., 48 (aa). p. 495; 1862. 



Bingkaml 
Jackson J 



Viscosity Standards 

TABLE 8 
Viscosity in Centipoises of Alcohol-Water Mixtures 



77 





Weight, percentage of ethyl alcohol 


Tem- 
perature, 

°C 





10 


20 


30 


39 


40 


1 
45 1 50 

! 


60 


70 


80 


90 


100 


Volume, percentage of ethyl alcohol at 25° C 







12.36 


24.09 


35.23 


44.92 


45.83 


50.94 


55.93 


65.56 


74.80 


83.59 


92.01 


100 




5 

10 

15 

20 

25 

30 

35 

40 

« 

50 

55 

60 

65 

70 

75 

80 


1.792 
1.519 
1.308 
1.140 
1.005 
.894 
.801 
.722 
.656 
.599 
.549 
.507 
.469 
.436 
.406 
.380 
.356 


3.311 
2.577 
2.179 
1.792 
1.538 
1. 323 
1.160 
1.006 
.907 
.812 
.734 
.663 
.609 
.554 
.514 
.476 
.430 


5.319 
4.065 
3.165 
2.618 
2.183 
1.815 
1.553 
1.332 
1.160 
1.015 
.907 
.814 
.736 
.666 
.608 
.559 
.505 


6.94 
5.29 
4.05 
3.26 
2.71 
2.18 
1.87 
1.58 
1.368 
1.189 
1.050 
.929 
.834 
.752 
.683 
.624 
.567 


7.25 
5.62 
4.39 
3.52 
2.88 
2.35 
2.00 
1.71 
1.473 
1.284 
1.124 
.993 
.885 
.798 
.725 
.660 
.598 


7.14 
5.59 
4.39 
3.53 
2.91 
2.35 
2.02 
1.72 
1.482 
1.289 
1.132 
.998 
.893 
.802 
.727 
.663 
.601 


6.94 

5.50 

4.35 

3.51 

2.88 

2.39 

2.02 

1.73 

1.495 

1.307 

1.148 

1.016 

.907 

.816 

.740 

.672 

.609 


6.58 
5.26 
4.18 
3.44 
2.87 
2.40 
2.02 
1.72 
1.499 
1.294 
1.155 
1.020 
.913 
.818 
.740 
.672 
.612 


5.75 
4.63 
3.77 
3.14 
2.67 
2.24 
1.93 
1.66 
1.447 
1.271 
1.127 
.997 
.902 
.806 
.729 
.663 
.604 


4.762 

3.906 

3.268 

2.770 

2.370 

2.037 

1.767 

1.529 

1. 344 

1.189 

1.062 

.943 

.856 

.766 

.695 

.636 


3.690 

3.125 

2.710 

2.309 

2, 008 

1.748 

1. 531 

1.355 

1.203 

1.081 

.968 

.867 

.789 

.711 

.650 

.600 


2.732 

2.309 

2.101 

1.802 

1.610 

1.424 

1.279 

1.147 

1.035 

.939 

.848 

.764 

.704 

.641 

.589 

.546 


1.773 

1.623 

1.466 

1.332 

1.200 

1.096 

1.003 

.914 

.834 

.764 

.702 

.644 

.592 

.551 

.504 

.471 













VII. VISCOSITY OF SUCROSE SOLUTIONS 

The first sucrose solution used was 39.99 per cent sucrose by 
weight in vacuo. The results obtained are given in Table 9 and 
plotted in Figs. 4 and 5. The first column shows whether the left 
or the right limb was emptying, the second column gives the cor- 
rected time of flow in seconds, the third column gives the corrected 
pressure, while the fourth column gives the pressure used up in 
overcoming the viscous resistance, and the fifth column gives the 
fluidity calculated for the measured temperature given in the 
sixth column. In the last column the temperatures 24 are calcu- 
lated corresponding to these fluidities, using the formula 

14^8.6 
t = (<p + 20) 0.597 - -j~^ + 38.24 

The agreement between the observed and calculated values is 
good. 

Were the fluidity concentration curves linear they would 
follow the dotted lines. That the observed curves depart so 

u The temperatures are calculated instead of fluidities purely for the sake of convenience in the use of 
the formula. 



78 



Bulletin of the Bureau of Standards 



Vol. t 4 



K 



51 



3 50 






























1 






/ 




FLUIDITY-TEMPERATURE RE- 
LATION FOR VARIOUS CON- 
CENTRATIONS OF SUCROSE. 


















/ 


















/ 


/ 


















/ 


















j\ 


f 




300 














/ 
















} 


t 


















/ 


















/ 


















/ 










150 














































/ 








































/ 






































/ 










































1/ 
















200 






















$/ 






































/ 














/ 




























/ 












A 


/ 


























/ 














/ 


























/ 


r 












/ 










150 


















/ 












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o ^o o 40° 

TEMPERATURE 



60' 



80° 



100°C 



FlG. 4. — Showing the relation between fluidity and temperature for solutions of various 

sucrose content 



Bingham! 
Jackson J 



Viscosity Standards 



79 



widely from the linear is an indication of the chemical hydration 

of the sugar. 

TABLE 9 

Fluidity of a 39.99 Per Cent Sucrose Solution at Various Temperatures 



Limb 


Time.t 


Pressure, 
P 


Pressure, 
P 


Fluidity, 


Tempera- 
ture 
measured 


Tempera- 
ture 
calculated 


L 


Seconds 

3, 487. 8 

3,437.1 

2,236.4 

2, 199. 7 

1, 486. 7 

1, 477. 8 

1, 266. 1 

1,250.4 

918.1 

908.4 

730.6 

747.3 

543. 3 

545.8 

437.1 

437.3 

363.7 

363.2 

306.3 

307.3 

257.8 

257.2 


290. 65 

292. 97 
289. 15 

293. 43 

291. 94 
293. 19 
286. 44 
289. 92 
286. 39 
289. 24 
288. 74 
289. 17 

283. 34 

284. 76 

284. 33 

285. 07 
282. 29 
283.14 
280. 13 
279. 58 

282. 76 

283. 08 


290. 65 

292. 97 
289. 11 

293. 39 

291. 85 

293. 10 
286. 32 
289. 80 
286. 16 
289. 01 
288. 40 
288. 83 

282. 71 
284. 13 

283. 34 

284. 08 

280. 85 

281. 70 

278. 11 
277. 56 
279. 93 
280. 25 


6.89 
6.94 
10.81 
10.83 
16.11 
16.14 
19.28 
19.29 
26.58 
26.60 
35.09 
35.21 
45.09 
45.07 
56.18 
56.26 
68.43 
68.32 
82.05 
81.95 
96.86 
96.97 


0.32 
.46 
9.96 
9.96 
19.98 
19.98 
24.99 
24.99 
35.00 
35.00 
45.00 
45.00 
54.99 
54.99 
64.96 
64.96 
74.94 
74.94 
85.03 
85.03 
95.30 
95.30 


°C 
0.81 


R 


.94 


L 


9.94 


R 


9.98 


L 


19.96 


R 


20.00 


L 


25.07 


R 


25.08 


L 


35.17 


R 


35.19 


L 


44.92 


R 


45.14 


L 


55.00 


R 


54.98 


L 


64.83 


R 


64.91 


L 


74.76 


R 


74.69 


L 


85.39 


R 


84.99 


L 


95.69 


R 


95.77 







The values of the fluidity given above do not agree with the 
values obtained by other observers, as will be shown later, hence 
the viscometer was tested with pure water and another series of 
measurements were made with an entirely new solution, which, 
however, happened to have the same concentration as the former, 
viz, 39.99 per cent by weight. 

TABLE 10 
Fluidity of a Second 39.99 Per Cent Sucrose Solution at Various Temperatures 



Limb 


Time, t 


Pressure, 
P 


Pressure, 
P 


Fluidity, 


Tempera- 
ture 
observed 


Tempera- 
ture 
calculated 


L 


Seconds 

2,024.4 

1, 256. 4 

1,232.4 

1,045.3 

1,039.8 

770.6 

768.4 

594.0 

593.1 


257. 97 
288. 16 
293. 15 

293. 24 

294. 43 

295. 00 
295. 41 
294. 30 
294.63 


257. 92 
288. 04 
293. 02 
293. 04 
294.27 
294.65 
295. 10 
293.73 
294.10 


13.39 
19.31 
19.36 
22.82 
22.84 
30.78 
30.82 
40.06 
40.07 


°C 

14.97 
24.99 
24.99 
30.00 
30.00 
40.00 
40.00 
50.00 
50.00 


°C 
15.10 


L 


25. 12 


R 


25.18 


L 


30.10 


R 


30.24 


L 


40.23 


R 


40.27 


L 


50.14 


R 


50.15 







8o 



Bulletin of the Bureau of Standards 



voi.14 



The second sample gave values which correspond very well with 
the former values, hence we have additional reason for confidence 
in the reliability of our values. It should be noted in this con- 
nection that Bingham, Schlesinger, and A. B. Coleman, 25 using a 
viscometer of different construction, have already noted that the 
observations of Hosking on sugar solutions may be in error. This 
was confirmed by the measurements of C. Coleman. 25 





















































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Fig. 5. — Showing relation between fluidity and sucrose content at various temperatures 

Having found an appreciable difference between our own values 
and those of other observers, it seemed desirable to measure the 
fluidity of a 20 per cent solution, the concentration actually 
obtained being 20.007 P er cent. The fluidities are given in Table 
1 1 . The last observation recorded in the table was made several 
hours after the preceding observation, when the solution had cooled 
down from the high temperature. The fluidities are again con- 
siderably smaller than the values found by Hosking. 

»Loc. cit. 



Bingkaml 
Jackson J 



Viscosity Standards 



81 



TABLE 11 
Fluidity of a 20.007 Per Cent Sucrose Solution at Various Temperatures 



Limb 


Time, t 


Pressure, 
P 


Pressure, 
P 


Fluidity, 


Tempera- 
ture 


L 


Seconds 
899.1 
897.0 
643.4 
644.2 
414.7 
415.5 
263.4 
261,4 
324.5 
324.3 
217.8 
215.8 
201.3 
200.5 
213.1 
212.4 
248.4 
247.4 
1, 783. 8 


290 43 
290. 86 
289. 26 
288. 77 
288.42 

287. 77 
288. 91 

288. 89 
288. 52 

288. 71 
287. 93 

289. 86 
262. 51 
262.86 
212. 40 
212. 84 
157. 68 
158. 13 

76.92 


290. 21 
290.64 
288. 83 
288. 34 
287. 38 
286. 73 
286.35 
286. 29 

286. 82 

287. 01 
284. 20 
286. 06 
258. 17 
258. 48 
208. 55 
208.96 
154. 86 
155. 29 

76.86 


26.79 
26.81 
37.61 
37.63 
58.65 
58.67 
75.10 
75.09 


°C 

0.44 


R 


.44 


L 


9.96 


R 


9.96 


L 


24.99 


R 


24.99 


L 


35.00 


R 


35.00 


L 


45.00 


R 


93.40 

112. 92 
113. 22 
134. 50 
134. 89 
157. 28 
157. 48 
181. 72 

181. 93 
50.98 


45.00 


L 


54.99 


R 


54.99 


L 


64.96 


R 


64.96 


L 


74.94 


R 


74.94 


L 


85.03 


R 


85.03 


L 


19.98 







Table 12 contains the results of measurements of the fluidity 
of a solution which contained 59.94 per cent sucrose by weight. 
This concentration has not been measured over a range of tem- 
peratures by previous observers. 

TABLE 12 
Fluidity of a 59.94 Per Cent Sucrose Solution at Various Temperatures 



Limb 


Time, t 


Pres- 
sure, p 


Pres- 
sure, P 


Fluidity, 


Tem- 
perature 
observed 


Tem- 
perature 
calculated 


L 


Seconds 

26, 023 

10, 310 
6,222 
4,029 
2, 736. 6 
1,957.2 
1, 392. 
1,111.3 
870.6 
1, 508. 4 


295. 87 

296. 61 
295. 76 
295. 50 

295. 89 

296. 22 
295. 67 
295. 65 
295. 84 
289. 45 


295. 87 

296. 61 
295. 75 
295. 49 
295. 86 
296. 17 
295. 56 
295. 48 
295. 57 
289. 34 


0.908 
2.286 
3.798 
5.871 
8.633 
12. 058 
[16. 989] 
21. 286 
27. 162 
16. 015 


°C 

9.96 
24.99 
35.00 
45.00 
54.99 
64.96 
74.94 
85.03 
95.30 
74.94 


°C 
11.61 


R 


24.99 


L 


34.84 


R 


44.90 


L 


54.99 


R 


64. 79 


L 


76.30 


R 


85.03 


L 


95.92 


L 


74. 18 







On calculating out the above data it was seen that the measure- 
ment at 74. 94 was manifestly in error, hence the last observa- 
tion in the table was made on the same solution two days later, it 



82 



Bulletin of the Bureau of Standards 



Vol.14 



having remained at room temperature in the meantime. The 
temperatures in the last column were calculated by means of the 
formula 

T= (^ + 5)1.472 = ?-;*-■? + 58.62 

It was easy to keep the solution at a temperature which was 
constant within one-tenth of a degree, hence the formula does not 
serve to reproduce the observed values satisfactorily. We may add 
that in so viscous a solution the fluidity is greatly affected by the 
temperature, a rise of i° at 45 causing an increase of 4.1 per 
cent in the fluidity. 

A 60 per cent solution was now prepared from commercial 
sugar in order to learn whether an}- serious error would be made 
in using commercial sugar instead of specially prepared sugar. 
The solution proved to be 60.17 P er cen t sucrose. The fluidity 
is given in Table 1 >• 

TABLE 13 

Fluidity of a 60.17 Per Cent Solution of Commercial Sugar at 74.94° C 



1 
Limb j Time, t 


Pres- 
sure, p 


Pres- 
sure, P 


Fluidity, 


Tem- 
perature 
observed 


L 


Seconds 
1,484.6 


292.91 


292.80 


16.08 


°C 
74.94 











For convenience in comparison the observed fluidities were 
plotted to a large scale and interpolated for even concentrations 
and for every 5 . The resulting fluidities are given in Table 14 
and the corresponding viscosities are given in Table 15. 

TABLE 14 

Fluidities of Sucrose Solutions Containing 0, 20, 40, and 60 Per Cent Sucrose by 
Weight at Every 5° C (Interpolated) 



Temper- 


Percentage sucrose by weight 


Temper- 
ature, "C 


Percentage sucrose by weight 


ature, °C 


1 
0a 20 


40 


. 





20 


40 


60 




5 . 

10 

15 

20 

25 

30 


55.91 
65.99 
76.56 
87.67 
99.54 
111.84 
124. 70 


26.29 
31.71 
37.71 
44.11 
51.02 
58.69 
66.51 
75.12 
83.82 
93.42 
103. 07 


6.77 
8.65 
10.21 
13.39 
16.13 
19.28 
22.82 
26.58 
30.78 
35.13 
40.05 


0.42 
.64 
.91 
1.34 
1.77 
2.28 
2.96 
3.77 
4.70 
5.82 
7.14 


• 

60 

65 

70 

75 

80 

i 85 

90 

i 100 


197. 16 
212. 72 
229. 41 
246.18 
263.57 
281.21 
299.31 
317. 87 
335.46 
354. 49 


113. 12 
123. 79 
134.81 
145. 97 
157. 56 
169. 53 
181.80 


45.06 
50.47 
56.24 
62.17 
68.41 
74.96 
81.92 
89.06 
96.41 
104.11 


8.57 
10.17 
11.99 
13.98 
16.12 
13.51 
21.14 


35 


■\\<* 70 


24.07 


40 l«a r>7 




26.85 


4 5 


167. 84 
181.92 




29.96 


50 







a These are the average fluidities calculated from Table 5. 



Bingkaml 
Jackson J 



Viscosity Standards 



83 



TABLE 15 



Viscosities in Centipoises of Sucrose Solutions Containing 0, 20, 40, and 60 Per Cent 
Sucrose *by Weight at Every 5° C (Interpolated) 



Temper- 


Percentage sucrose by weight 


Temper- 
ature, °C 


Percentage sucrose by weight 


ature, °C 


0« 


20 


40 


60 





20 


40 


60 




5 

10 

15 

20 

25 

30 

35 


1.789 
1.516 
1.306 
1.141 
1.005 
.894 
.802 
.720 
.653 
.596 
.550 


3.804 
3.154 
2.652 
2.267 
1.960 
1.704 
1.504 
1.331 
1.193 
1.070 
.970 


14.77 
11.56 
9.794 
7.468 
6.200 
5.187 
4.382 
3.762 
3.249 
2.847 
2.497 


238 

156 

109.8 
74.6 
56.5 
43.86 
33. 78 
26.52 
21.28 
17. 18 
14.01 


55....... 

60 

65 

70 

75 

80 

85 

90 

95 

100 


0.507 
.470 
.436 
.406 

.379 
.356 
.334 
.315 
.298 
.282 


0.884 
.808 

.742 
.685 
.635 
.590 
.550 


2.219 
1.982 
1.778 
1.608 
1.462 
1.334 
1.221 
1.123 
1.037 
.960 


11.67 
9.83 
8.34 
7.15 
6.20 
5.40 
4.73 
4.15 


40 




3.72 


45 




3.34 


50........ 







o These are the average viscosities given in Table 5. 

We reproduce here for the sake of comparison the viscosities of 
sugar solutions obtained by Hosking, 26 Table 16, and by Powell, 27 
Table 17. Burkhardt, 28 Rudorf, 29 Griineisen, 30 and Green 31 have 
studied the viscosity of sugar solutions, but not over a range of 
temperatures. The viscosities determined by Hosking are gen- 
erally considerably lower than our values, although it is to be 
noted that we agree with Hosking satisfactorily at the lowest 
temperature in the 40 per cent solution and at the highest tempera- 
ture in the 20 per cent solution. The values of Powell, are, in 
general, intermediate between Hosking's values and our own, but 
agree better with the former. Bingham, Schlesinger, and Coleman 
obtained 1.731 cp for the viscosity of a 20 per cent sugar solution 
at 2 5 C using the Washburn viscometer. This is considerably 
higher than the present value. 

26 Phil. Mag. [5], 49, p. 274; 1900. 

27 Trans. (London) Chem. Soc, 105, p. 1; 1914. 

28 Zs. Rubenzuckerind. 1874. Cf. Castell- Evans Physieo-Chemical Tables, 2, p. 652; 1911, 

29 Zs. physik. Chem., 43, p. 281; 1903. 

30 Wiss. Abh. d. Phys.-Tech. Reichsanstalt, 4, p. 239; 1905. 

31 Trans. (I,ondon) Chem. Soc., 93, p. 2023; 1908. 



84 Bulletin of the Bureau of Standards 

TABLE 16 
Viscosity of Sucrose Solutions in Centipoises According to Hosking j: 



V*. 14 



Teaper*tur». * C 



:: 









ft M 


:. a 


3.720 


L729 


2.050 


3.042 


: -l: 


L754 


2.578 


L292 


L518 


2.212 


L139 


: v.\ 


L910 


LOW 






.901 


1.041 


L485 


.Ml 


.933 


L319 


.-:: 


.843 


:.::■: 


.663 


.763 


L059 


.611 


.699 


.961 


.SM 


.540 






.592 


.799 


.487 


.;-- 








.676 





.--■: 


. I ■ 


.359 


. --■ 


.586 


:-- 


-:. 




.349 


. :. : ; 





1.810 

5 L537 

L 331 

15 ! L168 

20 ' 1.031 

25 

30 812 

35 

40 

609 

50 555 

55 

60 

65 438 



75 387 

8D 362 

85 Ml 





14.76 
1L33 
8.95 
7.30 
6.07 
5.08 

- ;:: 
L€a 

1 m 

2.728 
2.410 
1 M 
L908 

L553 

L414 
L ■ 

1.182 
L093 



TABLE 17 

Viscositr r5 According tD Powell ■ 



— 




- 


;: 


:- 




-: 


: 




1.17 
LOS 

- 


LOO L18 
.90 L06 


::: 

L6i 
1.43 

L28 

1.15 






s: 

35 

40 

45 

5} 


- 
.67 
.61 


.:: 

.'■: 

n 

- :: 


L83 
L62 

L44 


2.08 





Same Solutions at 20 : According to Burkhardt 



: . 



:. :■■:: :.::: . :-:•- :-:: 2. :-: 



From the data of Green 3 - we calculate the viscosity of a 40 per 
cent solution to be 6.0S cp at 20° and 5.066 cp at : 

We have not attempted to apply any corrections to the above 
data, but the probable corrections would tend to decrease the 



c Loc dt. 



/ST] Viscosity Standards 85 

viscosity, hence they would not help to bring about agreement 
between our values and those of earlier observers. 

In connection with the fact that our viscosities are in this case 
higher than those of most of our predecessors, it is of interest to 
note that when the viscosity of the commercial sugar solution used 
by us was reduced to the basis of a 60 per cent solution at 75 ° C, 
we obtain 6.07 cp, which is also lower than the 6.20 obtained by 
us for specially purified sugar. 

In the appendixes are given tables of densities of sucrose and 
ethyl-alcohol solutions, reproduced here for the convenience of any 
who may desire to use the data given in this paper for the purposes 
of calibration. 

VIII. SUMMARY 

1. For the purpose of the calibration of viscometers, there is 
need for one or more liquids whose viscosity is greater than that 
of water, which can be easily obtained, and whose viscosity is 
known with a considerable degree of certainty. 

2. Of the suitable substances ethyl alcohol- water mixtures and 
sucrose solutions each possess certain marked advantages. The 
viscosities of the former are well known, there existing data by 
several observers which agree as well as can be expected; but the 
correctness of the data for the latter has been questioned. Hence 
we have redetermined the viscosity of a 20 and a 40 per cent 
solution by weight and have in addition measured the viscosity of 
a 60 per cent solution from io° to 95 ° C. The viscosities obtained 
by us are generally somewhat higher than the values obtained 
hitherto, but we have every reason to believe that our values are 
worthy of confidence. 

3. The existing data on the viscosity of water has been reviewed 
in order to correct it so far as possible according to our present 
knowledge. The viscosity and fluidity of water for every degree 
centigrade from o to 100 has been calculated. 

4. The advantages and disadvantages of expressing viscosity in 
absolute or specific units have been compared. The suggestion 
has been made that by expressing all data in terms of the centi- 
poise (the one-hundredth part of the cgs unit), the absolute vis- 
cosity of substances would be practically also the specific viscosity, 
provided that we take water at 20 as the standard. We find the 
most probable value for the viscosity of water at 20 C to be 
1.005 C P- 

Washington, August 8, 191 6. 



APPENDIXES 

Appendix A. — Density in Grams per Milliliter of Mixtures of Ethyl Alcohol and Water 

Per cent alcohol by weight 10° C 15° C 




5 
10 
IS 

n 

25 

90 
35 
40 
IS 

50 

55 

CO 

f5 

:o 

"5 
BO 
85 

90 
95 

IOC 



0.99973 
9098 
8393 
7800 
7252 
6665 
5977 
5162 
4238 
3226 
2162 
1055 

.89927 
8774 
7602 
6408 
5197 
3951 
2654 
1278 

. 79784 



0.99913 
9032 
8304 
7669 
7068 
6424 
5686 
4832 
3882 
2852 
1776 
0659 

. 89523 
8364 
7187 
5988 
4772 
3525 
2227 
0852 

. 79360 



20° C 


25° C 


30° C 


35° C | 


0. 99823 


0. 99708 


0. 99568 


0.99406 


8938 


8817 


8670 


8501 


8187 


8043 


7875 


7685 


7514 


7334 


7133 


6911 


6864 


6639 


6395 


6134 


6168 


5895 


5607 


5306 


5382 


5067 


4741 


4403 


4494 


4146 


3790 


3425 


3518 


3148 


2770 


2385 


2472 


2085 


1692 


1291 


1384 


0985 


0580 


0168 


0258 


. 89850 


.89437 


.89016 


.89113 


8699 


8278 


7851 


7948 


7527 


7100 


6667 


6766 


6340 


5908 


5470 


5564 


5134 


4698 


4257 


4344 


3911 


3473 


3029 


3095 


2660 


2220 


1774 : 


1797 


1362 


0922 


0478 | 


0424 


. 79991 


. 79555 


.79114 | 


.78934 


8506 


8075 


7641 ; 



0.99225 
8311 
7475 
6670 
5856 
4991 
4055 
3051 
1992 
0884 
.89750 



7417 
6227 
5025 
3809 
2578 
1322 
0028 
78670 
7203 



33 This Bulletin, 9, p. 327; 1913. 

Appendix B. — Density in Grams per Milliliter of Sucrose Solution 



Per cent 

sucrose by 

weight 



0°C 


10° C 


15° C 


20° C 


25° C 


0. 99987 


0. 99973 


0.99913 


0. 99S23 


0. 99707 


1. 02033 


1. 01960 


1.01884 


1. 01784 


1.C1661 


4135 


4016 


3925 


3813 


3679 


6304 


6146 


6041 


5916 


5772 


8546 


8353 


8233 


8094 


7940 


1. 10869 


1. 10642 


1. 10507 


1. 10354 


1. 10188 


3274 


3014 


2863 


2698 


2517 


5769 


5473 


5306 


5127 


4933 


8349 


8020 


7837 


7648 


7439 


1. 21018 


1. 20657 


1.20460 


1. 20257 


1. 20039 


3775 


3382 


3173 


2958 


2732 


6621 


6203 


5981 


5753 


5516 


9560 


9117 


8884 


8644 


8399 


1. 32591 


1.32125 


1. 31882 


1.31631 


1. 31376 


5719 


5230 


4976 


4716 


4452 



30° C 



40° C 



50° C 



60° C 



c 

5 
lfl 

15 

20 
IS 

9C 
35 
40 
45 
50 
55 
60 
§5 

70 



0. 99567 

1.01518 
3530 
5612 
7767 

1.10005 
2324 
4730 
7214 
9812 

1.22495 
5271 
8144 

1.31113 
4181 



0. 99232 
1.01169 

3165 
5229 
7366 
9585 

1. 11888 

4279 
6759 
9332 

1.21996 
4756 
7615 

1.30571 
3625 



0. 98813 

1. 00735 

2720 
4772 
6898 
9106 I 

1. 11398 , 
3779 ! 
6248 j 
8811 j 

1.21465 i 
4211 j 
7058 j 

1.30002 I 
3047 



0. 98330 
1.00231 

2198 
4238 
6358 
8563 

1.10850 
3228 
5693 
8247 

1.20891 
3629 
6468 
9408 

1. 32447 



M Plato. Abh. Norm. Eich.-Komm., 2, p. 140. 1900; Zs. Zuckerindustrie. 50, pp. 982 and 1079, 1900; cf. Lan- 
dolt and Bornstein's Physikalisch-Chemische Tabellcn, fourth ed., p. 311. 

86 



^MSi^l